Cauchy and periodic unilateral problems for aging linear viscoelastic materials

Abstract

Our aim in this paper is to study the Gauchy-Signorini problem and the periodic Signorini problem for a class of linear viscoelastic materials with aging and fading memory defined in Section 1. In classical linear elasticity with infinitesimal displacements the Signorini problem corresponds to contact without friction and gives rise to unilateral boundary conditions studied with variational inequalities (see [12] and its bibliography). The results obtained in Section 3 for the Cauchy-Signorini problem complete the work of Duvaut [I I] for hereditary linear viscoelastic materials with fading memory but the study of the periodic Signorini problem seems new even in this particular case. A particular feature of the periodic problem for Maxwell-type materials, whose constitutive laws can be written